The Spanish giants have supplied Liverpool with the same number of tickets they controversially gave Chelsea last term, with their ground undergoing significant redevelopment - risking the ire of another British club.
Releasing a statement on their website on Tuesday, Liverpool said that the allocation they had been handed was "significantly less than expected".
"This allocation is significantly less than expected for this game," the club said.
"The club has contacted UEFA and Real Madrid regarding the reduced allocation to understand the rationale behind this decision.
"Spirit of Shankly, the official Supporters Trust, and the Liverpool Disabled Supporters Association have also asked the club to raise their concerns and asked to remain in dialogue throughout the process," they added.
"LFC is committed to having as many supporters as possible in stadiums for European away fixtures and continues to develop its systems and processes to fill allocations at every away game.
"The club fully understands the impact this initial decision by Real Madrid has on supporters and the challenges with making travel arrangements for the game.
"Representatives from LFC are in direct contact with the Supporters Trust and the Liverpool Disabled Supporters Association and will continue to explore all options to increase the allocation, particularly for disabled supporters.
"LFC will provide supporters with an update when the ticket allocation has been confirmed."